4.Pressure Tank?
Bladder or diaphragm tank (one pipe to tank)_____yes
Size or model of tank_____9 gal.
Air charge in top of tank, with pump off and water drained_________18___PSI
(check with car tire gauge)

I installed a shut off valve after the pump and tank. When I shut off the valve, the pump holds pressure and never cycles. Once I turn the valve on the pressure gradually drops to 20psi and comes on without anybody using any water. This takes about 10 or 15 minutes.

This is a really old house so 95 % of the pipes are visible and nothing seems to be leaking. All the cold water pipes are new and the toilet is shut off. The faucets do not drip and there's no visible leak at the hot water tank (electric) or anywhere else.

I was wondering if there is something wrong with the hot water tank causing some kind of pressure drop.

Sounds like you have a leak you need to find. How much pipe do you have underground? House on a slab? Turn the water off to the water heater and eliminate any possibility of a hot water leak. If you have a valve outside the house before the main water line comes into the house you could turn that valve off and see if you still lose pressure. If you still lose pressure and the valve is workign you know the leak is between the valve and the pump.

The pipe from the pump to the bottom of the well is straight down from the pump. The well is in the house. There is no valve outside the house. The pump works like it should with no leaks at all. When I open the valve between the pump/tank and the house plumbing is when I have a problem so it definetly has nothing to do with the pump itself. I can't check the hot water tank now but it will check it out as soon as I can. thanks for the reply

Hmm, you have a leak somewhere. If you had a leak that big in the water heater you would have water on the floor. You still need to rule out the toilets. Don't trust that the shutoffs work. Flush the toilet too so that there is no water in the toilet tank. Check and make sure it does not fill back up with the shutoffs closed.

Do you have a humidifier on the furnace? Do any pipes go outside to a faucet or irrigation system? DO any of the water pipes run under the basement floor or slab? How about floor drains in the basements? Some floor drains have a water connection to keep the trap from drying out.

I guess the toilet shut off is the only possible problem but I will still check the HW tank just to be sure.

There is no furnace in this house just a wood stove.

The plumbing in the house comes from the pump under the kitchen cabinet, goes to the HW tank then to the kitchen sink and then hot and cold the the bathroom that's it. Nothing going outside or under the house. All the pipes are visible except for one spot that goes through a floor but there's no leaks there.